This is a good question. I am curious to see what others say too.

Because I can also sometimes get caught up in questions of reality and perception, I have instead decided to define things as "real to me," "real to you," and "real to everyone," and leave it at that.

One sort of reality check you can do, is to ask yourself, "is this unusual?" But this is only useful some of the time. If you had never seen a llama trotting down the hall of the nursing home before, and you saw one today, you would probably recognize it as unusual, and pause before responding.
But in the case of entirely plausible situations, such as an ordinary looking person saying "hi" to you, it can be extremely difficult to tell. One thing I have done is to train myself to greet others with eye contact and a smile, rather than a verbal greeting, if it is the first time I am seeing them, or I have any question about their state of realness. It's much easier to shrug off, and it buys you a little time to see if, and how others react, which may help you gauge how you yourself respond.

I also think it's okay in most scenarios, to ask someone else, "did you hear/see/feel that?" If they say no, you can usually say it must have been that tv/headlight reflection/vent coming on, etc.

btw I also work in a nursing home. I enjoy it very much. Do you?